Question

BO, US, and IR are all medians of triangle BSR. If BT is 12 units long, how long is OT? BO? If IR is 18 units long, how long is IT? TR? If UT is 9 units long (the shortest piece), how long is TS? US? If BU is (4x - 6) units long and RU is (2x + 12) units long, how long is BR?

A) OT = 6 units, BO = 12 units, IT = 9 units, TR = 18 units, TS = 9 units, BR = 14x - 6 units
B) OT = 6 units, BO = 24 units, IT = 27 units, TR = 12 units, TS = 15 units, BR = 2x + 12 units
C) OT = 3 units, BO = 18 units, IT = 12 units, TR = 27 units, TS = 6 units, BR = 6x + 18 units
D) OT = 12 units, BO = 6 units, IT = 18 units, TR = 9 units, TS = 24 units, BR = 4x + 12 units

Answer 1

To find the lengths of various medians in triangle BSR, we can use the given information and the properties of medians. By dividing the lengths of segments and applying algebra, we can determine the lengths of OT, BO, IT, TR, TS, and BR.

Step-by-step explanation:

The question is about finding the lengths of various medians in a triangle. We are given the lengths of some medians and asked to find the lengths of others. Let's break down the problem step by step:

1. First, we find the length of OT. Since OT is a median, it divides BT into two equal parts. Therefore, OT = BT/2 = 12/2 = 6 units.
2. Next, we find the length of BO. Since BO is a median, it divides RS into two equal parts. Therefore, BO = RS/2 = 24/2 = 12 units.
3. Next, we find the length of IT. Since IT is also a median, it divides SR into two equal parts. Therefore, IT = SR/2 = 18/2 = 9 units.
4. Similarly, TR is also a median, so TR = BS/2 = 36/2 = 18 units.
5. TS is the longest piece of the median US, so TS = US - UT = 2(9) - 9 = 9 units.
6. Finally, BR is the sum of BU and UR, so BR = BU + UR = 4x - 6 + 2x + 12 = 6x + 6 units.

Therefore, the correct answer is option A: OT = 6 units, BO = 12 units, IT = 9 units, TR = 18 units, TS = 9 units, BR = 14x - 6 units.